document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=641779>Question 641779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line passing through (3,5) that makes an angle of 45(degrees) with the positive x-axis? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403876 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=403876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope of a line is the tangent of the smaller angle it makes with the positive x-axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C0.7%2C1.7%2C-0.2%2C0.8%2C%0D%0Agrid%280%29%2C%0D%0Ablue%28line%280.7%2C-0.1%2C1.7%2C0.9%29%29%2C%0D%0Agreen%28triangle%280.8%2C-0.01%2C1.3%2C0.49%2C1.3%2C-0.01%29%29%2C%0D%0Alocate%280.85%2C0.05%2Cangle%29%2C%0D%0Alocate%280.99%2C-0.002%2CDELTAx%29%2Clocate%281.31%2C0.3%2CDELTAy%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > In the green right triangle, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28angle%29=DELTAy%2FDELTAx=slope ALIGN=MIDDLE  ALT=\"tan%28angle%29=DELTAy%2FDELTAx=slope\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2845%5Eo%29=1 ALIGN=MIDDLE  ALT=\"tan%2845%5Eo%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope of the line<BR>\n" );
document.write( "The point-slope form of the line we want, using point (3,5) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=1%2A%28x-3%29 ALIGN=MIDDLE  ALT=\"y-5=1%2A%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=x-3 ALIGN=MIDDLE  ALT=\"y-5=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and adding 5 to both sides of the equal sign,<BR>\n" );
document.write( "we get the equivalent, more popular,and unique slope-intercept form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=x%2B2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-3%2C7%2C-2%2C8%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28circle%283%2C5%2C0.2%29%29%2C%0D%0Ablue%28line%28-3%2C-1%2C7%2C9%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );